Understanding the Side Ratio of a 30-60-90 Triangle: Explained with Examples

The side ration of a 30-60-90 triangle is …

The side ratio of a 30-60-90 triangle is a specific ratio that applies to the lengths of the sides in this type of triangle

The side ratio of a 30-60-90 triangle is a specific ratio that applies to the lengths of the sides in this type of triangle. In a 30-60-90 triangle, the angles measure 30 degrees, 60 degrees, and 90 degrees respectively.

The side lengths in a 30-60-90 triangle are in a ratio of 1:√3:2. This means that the length of the shortest side (the one opposite the 30-degree angle) is 1 unit, the length of the second longest side (the one opposite the 60-degree angle) is √3 units, and the length of the longest side (the one opposite the 90-degree angle, which is the hypotenuse) is 2 units.

To understand this ratio, we can use the property of right triangles, specifically the Pythagorean theorem. In a 30-60-90 triangle, the shortest side is half the length of the hypotenuse, and the second longest side is (√3)/2 times the length of the hypotenuse. These ratios can be derived by using the Pythagorean theorem and trigonometric functions.

For example, if the hypotenuse is 4 units long, the other two sides of the triangle would be:

Shortest side = (1/2) * 4 = 2 units.
Second longest side = (√3/2) * 4 = 2√3 units.

The side ratio of a 30-60-90 triangle can be used to find the lengths of the sides if you know the length of one side or the hypotenuse. Similarly, if you know the ratio, you can find the missing side lengths by multiplying the ratio with the known length.

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